Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/837

Rh for, in the time of one vibration, the earth, which is the quickest available vehicle, has only moved a distance of $$\tfrac{1}{10000}$$ of a wave-length; which is equivalent to a middle $$\mathrm{C}$$ fork sounding and creeping along at the rate of 15 inches an hour. No practical question as to imperfection in spherical form of wave from moving source is therefore likely to arise. See however § 19, for discussion of a question not of shape but of intensity.

There happen to be one or two interesting things connected with the reflexion of light from a moving source when there is some connexion established between the reflected ray and the subsequent position of the source, e.g., as when a ray is reflected back upon itself, with the object of causing interference; these are specially dealt with in §§ 59, 60.

Case of Source arid Receiver moving together through Stationary Medium; or, correlative case of Medium drifting past fixed Source and Receiver.

15. Consider a telescope fixed relatively to source, and medium drifting freely past both. The object-glass must be set skew to the wave front, but normal to the advancing ray or radius vector.

In fig. 4, $$\mathrm{SM}$$ is the axis of the telescope, and it points straight at the source. There is no resultant aberration, the object is seen in its true position.

It is also seen of its right colour, for the waves are carried to the receiver at their accustomed frequency: there is no Doppler effect. A steady wind alone is powerless to influence either direction or pitch.

But what about interference phenomena, depending on the time of a given journey? Manifestly a motion of the medium will be able to affect this, and may accordingly bring about the displacement of fringes representing hurry or lag of phase.

Consider a telescope fixed relatively to the source and placed so as to receive light along the radius vector $$r$$.

If the medium is stationary, the light journey is accomplished in the time

$\mathrm{T} = \tfrac{r}{\mathrm{V}}$,|undefined

but if moving, the time of the journey is

$\mathrm{T}^\prime = \tfrac{r}{\mathrm{V}\cos\epsilon + v\cos\theta}$,

and so there is a hurrying up of phase

$\tfrac{\mathrm{T}}{\mathrm{T}^\prime} = \cos\epsilon + \alpha\cos\theta$,|undefined or

$\mathrm{T} - \mathrm{T}^\prime \approx \alpha\mathrm{T}\cos\theta$.